Question

Item X is a standard item stocked in a company's inventory of component parts. Each year the firm, on a random basis, uses about 2,000 of item X, which costs $25 each. Storage costs, which include insurance and cost of capital, amount to $5 per unit of average inventory. Every time an order is placed for more of item X, it costs $10. a. Whenever item X is ordered, what should the order size be? b. What is the annual cost for ordering item X ? c. What is the annual cost for storing item X ?

Answer 1

a. The optimal order size can be determined using the economic order quantity (EOQ) formula:

EOQ = sqrt((2DS)/H)

Where:
D = annual demand = 2,000 units
S = order cost = $10 per order
H = holding cost = $5 per unit per year

Substituting the values:

EOQ = sqrt((2 x 2,000 x $10)/$5) = sqrt(8,000) = 89.4

Therefore, the optimal order size for item X should be 89 units.

b. The annual ordering cost can be calculated as:

Annual ordering cost = (Annual demand / EOQ) x Ordering cost per order

Annual ordering cost = (2,000 / 89) x $10 = $224.72

Therefore, the annual ordering cost for item X is $224.72.

c. The annual holding cost can be calculated as:

Annual holding cost = (EOQ / 2) x Holding cost per unit

Annual holding cost = (89 / 2) x $5 = $222.50

Therefore, the annual holding cost for item X is $222.50.